Weak isospin
Flavour in particle physics 

Flavour quantum numbers 

Related quantum numbers 

Combinations 

Flavour mixing 
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In particle physics, weak isospin is a quantum number relating to the electrically charged part of the weak interaction: Particles with halfinteger weak isospin can interact with the ^{}
_{}W^{±}
_{} bosons; particles with zero weak isospin do not.^{[a]}
Weak isospin is a construct parallel to the idea of isospin under the strong interaction. Weak isospin is usually given the symbol T or I, with the third component written as T_{3} or I_{3}.^{[b]}
It can be understood as the eigenvalue of a charge operator.
T_{3} is more important than T; typically "weak isospin" is used as short form of the proper term "3rd component of weak isospin".
The weak isospin conservation law relates to the conservation of weak interactions conserve T_{3}. It is also conserved by the electromagnetic and strong interactions. However, interaction with the Higgs field does not conserve T_{3}, as directly seen by propagation of fermions, mixing chiralities by dint of their mass terms resulting from their Higgs couplings. Since the Higgs field vacuum expectation value is nonzero, particles interact with this field all the time even in vacuum. Interaction with the Higgs field changes particles' weak isospin (and weak hypercharge). Only a specific combination of them, (electric charge), is conserved.
Relation with chirality[edit]
Fermions with negative chirality (also called "lefthanded" fermions) have and can be grouped into doublets with that behave the same way under the weak interaction. By convention, electrically charged fermions are assigned with the same sign as their electric charge.^{[c]}
For example, uptype quarks (u, c, t) have and always transform into downtype quarks (d, s, b), which have and vice versa. On the other hand, a quark never decays weakly into a quark of the same Something similar happens with lefthanded leptons, which exist as doublets containing a charged lepton (^{}
_{}e^{−}
_{}, ^{}
_{}μ^{−}
_{}, ^{}
_{}τ^{−}
_{}) with and a neutrino (^{}
_{}ν^{}
_{e}, ^{}
_{}ν^{}
_{μ}, ^{}
_{}ν^{}
_{τ}) with In all cases, the corresponding antifermion has reversed chirality ("righthanded" antifermion) and reversed sign
Fermions with positive chirality ("righthanded" fermions) and antifermions with negative chirality ("lefthanded" antifermions) have and form singlets that do not undergo charged weak interactions.^{[d]}
The electric charge, is related to weak isospin, and weak hypercharge, by
Generation 1  Generation 2  Generation 3  

Fermion  Symbol  Weak isospin 
Fermion  Symbol  Weak isospin 
Fermion  Symbol  Weak isospin 
Electron neutrino  Muon neutrino  Tau neutrino  
Electron  Muon  Tauon  
Up quark  Charm quark  Top quark  
Down quark  Strange quark  Bottom quark  
All of the above lefthanded (regular) particles have corresponding righthanded antiparticles with equal and opposite weak isospin.  
All righthanded (regular) particles and lefthanded antiparticles have weak isospin of 0. 
Weak isospin and the W bosons[edit]
The symmetry associated with weak isospin is SU(2) and requires gauge bosons with ( ^{}
_{}W^{+}
_{} , ^{}
_{}W^{−}
_{} , and ^{}
_{}W^{0}
_{} ) to mediate transformations between fermions with halfinteger weak isospin charges. ^{[2]} implies that ^{}
_{}W^{}
_{} bosons have three different values of
 ^{}
_{}W^{+}
_{} boson is emitted in transitions →  ^{}
_{}W^{0}
_{} boson would be emitted in weak interactions where does not change, such as neutrino scattering.  ^{}
_{}W^{−}
_{} boson is emitted in transitions → .
Under electroweak unification, the ^{}
_{}W^{0}
_{} boson mixes with the weak hypercharge gauge boson ^{}
_{}B^{0}
_{} ; both have weak isospin = 0 . This results in the observed ^{}
_{}Z^{0}
_{} boson and the photon of quantum electrodynamics; the resulting ^{}
_{}Z^{0}
_{} and ^{}
_{}γ^{0}
_{} likewise have zero weak isospin.
The sum of negative isospin and positive charge is zero for each of the bosons, consequently, all the electroweak bosons have weak hypercharge so unlike gluons of the color force, the electroweak bosons are unaffected by the force they mediate.
See also[edit]
Footnotes[edit]
 ^
Interaction with the ^{}
_{}Z^{0}
_{} is only related indirectly; its interaction is determined by weak charge, q.v.  ^
This article uses T and T_{3} for weak isospin and its projection.
 ^ Lacking any distinguishing electric charge, neutrinos and antineutrinos are assigned the opposite their corresponding charged lepton; hence, all lefthanded neutrinos are paired with negatively charged lefthanded leptons with so those neutrinos have Since righthanded antineutrinos are paired with positively charged righthanded antileptons with those antineutrinos are assigned The same result follows from particleantiparticle charge & parity reversal, between lefthanded neutrinos () and righthanded antineutrinos ().
 ^
Particles with do not interact with ^{}
_{}W^{±}
_{} bosons; however, they do all interact with the ^{}
_{}Z^{0}
_{} boson, with the possible exception of hypothetical sterile neutrinos not yet included in the Standard Model. If they actually exist, sterile neutrinos would become the only elementary fermions in the Standard Model that do not interact with the ^{}
_{}Z^{0}
_{} boson.
References[edit]
 ^
Baez, John C.; Huerta, John (2010). "The algebra of Grand Unified Theories". Bulletin of the American Mathematical Society. 47 (3): 483–552. arXiv:0904.1556. Bibcode:2009arXiv0904.1556B. doi:10.1090/s0273097910012942. S2CID 2941843.
 ^ An introduction to quantum field theory, by M.E. Peskin and D.V. Schroeder (HarperCollins, 1995) ISBN 0201503972; Gauge theory of elementary particle physics, by T.P. Cheng and L.F. Li (Oxford University Press, 1982) ISBN 0198519613; The quantum theory of fields (vol 2), by S. Weinberg (Cambridge University Press, 1996) ISBN 0521550025.